This Article 
 Bibliographic References 
 Add to: 
Line Art Illustrations of Parametric and Implicit Forms
January-March 1998 (vol. 4 no. 1)
pp. 71-81

Abstract—A technique is presented for line art rendering of scenes composed of freeform surfaces. The line art that is created for parametric surfaces is practically intrinsic and is globally invariant to changes in the surface parameterization. This method is equally applicable for line art rendering of implicit forms, creating a unified line art rendering method for both parametric and implicit forms. This added flexibility exposes a new horizon of special, parameterization independent, line art effects. Moreover, the production of the line art illustrations can be combined with traditional rendering techniques such as transparency and texture mapping. Examples that demonstrate the capabilities of the proposed approach are presented for both the parametric and implicit forms.

[1] M. D. Carmo, Differential Geometry of Curves and Surfaces. Prentice Hall, 1976.
[2] D. Dooley and M.F. Cohen, "Automatic Illustration of 3D Geometric Models: Lines," Computer Graphics, vol. 24, no. 2, pp. 77-82, Mar. 1990.
[3] D. Dooley and M.F. Cohen, "Automatic Illustration of 3D Geometric Models: Surfaces," Proc. Visualization '90, pp. 307-313.
[4] G. Elber, Free Form Surface Analysis Using a Hybrid of Symbolic and Numeric Computation, PhD dissertation, Computer Science Department, University of Utah, Salt Lake City, Utah, 1992.
[5] G. Elber, "Line Illustrations∈Computer Graphics," The Visual Computer, vol. 11, no. 6, pp. 290-296, 1995.
[6] G. Elber, "Line Art Rendering via a Coverage of Isoparametric Curves," IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 3, pp. 231-239, Sept. 1995.
[7] G. Elber and E. Cohen, "Arbitrarily Precise Computation of Gauss Maps and Visibility Sets for Freeform Surfaces," Proc. Third ACM/IEEE Symp. Solid Modeling and Applications, pp. 271-279,Salt Lake City, Utah, May 1995.
[8] G. Elber and E. Cohen, "Adaptive Iso-Curves Based Rendering for Free Form Surfaces," Trans. Graphics, vol. 15, no. 3, pp. 249-263, July 1996.
[9] P.N. Hasluck, Manual of Traditional Wood Carving.New York: Dover Publications, 1977.
[10] D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination, second ed. New York: Chelsea Publishing, 1990.
[11] J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design.Wellesley, Mass.: A.K. Peters, 1993.
[12] W.M. Ivins, How Prints Look, Photographs with Commentary, revised ed. Boston: Beacon Press, 1987.
[13] W.M. Ivins, Prints and Visual Communication, eighth printing. MIT Press, 1992.
[14] IRIT 6.0 User's Manual, Feb. 1996, Technion.
[15] J. Lansdown and S. Schofield, Expressive Rendering: A Review of Non-Photorealistic Rendering Techniques IEEE Computer Graphics and Applications, vol. 15, no. 3, pp. 29-37, May 1995.
[16] W. Leister, "Computer Generated Copper Plates," Computer Graphics Forum, vol. 13, no. 1, pp. 69-77, Mar. 1994.
[17] L. Markosian et al., "Real-Time Nonphotorealistic Rendering," Proc. Siggraph 97, Computer Graphics (Proc. Ann. Conf. Series), T. Whitted, ed., Addison Wesley, 1997, pp. 415-420.
[18] B.J. Meier, “Painterly Rendering for Animation,” SIGGRAPH '96 Conf. Proc., H. Rushmeier, ed., pp. 477-484, New Orleans, 1996.
[19] D. Mitchell, "Generating Antialiased Images at Low Sampling Densities," Computer Graphics, vol. 21, no. 4, pp. 65-72, 1987.
[20] O. Monga, S. Benayoun, and O. Faugeras, “From Partial Derivatives of 3D Density Images to Ridge Lines,” Proc. IEEE Conf. on Vision and Pattern Recognition, IEEE CS Press, Los Alamitos, Calif., 1992, pp. 354–359.
[21] D.R. Peachey, “Solid Texturing of Complex Surfaces,” Proc. SIGGRAPH 85, vol. 19, pp. 279-286, 1985.
[22] K. Perlin, “An Image Synthesizer,” Computer Graphics (SIGGRAPH '85 Proc.), B.A. Barsky, ed., vol. 19, no. 3, pp. 287-296, July 1985.
[23] Y.B. Pnueli and A.M. Bruckstein, "DigiDurer—A Digital Engraving System," The Visual Computer, vol. 10, pp. 277-292, 1994. Also CIS Report No. 9210, Computer Science Dept., Technion, Israel Inst. of Technology, June 1992.
[24] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in C.Cambridge, England: Cambridge Univ. Press, 1988.
[25] T. Saito and T. Takahashi, “Comprehensible Rendering of 3D Shapes,” Computer Graphics (Proc. Siggraph), Vol. 24, No. 4, Aug. 1990, pp. 197-206.
[26] L. Velho and J.M. Gomes, "Digital Halftoning with Space Filling Curves," Computer Graphics: Proc. Siggraph, vol. 25, no. 4, pp. 81-90, July 1991.
[27] G. Winkenbach and D.H. Salesin, “Computer-Generated Pen-and-Ink Illustration,” Computer Graphics (Proc. Siggraph), Vol. 28, No. 4, Oct. 1994, pp. 91-108.
[28] G. Winkenbach and D.H. Salesin, "Rendering Parametric Surfaces in Pen and Ink," Proc. Siggraph 96, ACM Press, 1996, pp. 469-476.
[29] A.P. Witkin and P.S. Heckbert, "Using Particles to Sample and Control Implicit Surfaces," Computer Graphics(Proc. Siggraph 94), vol. 28, no. 2, 1994, pp. 269-277.

Index Terms:
Sketches, illustrations, line drawings, freeform surfaces, NURBs, implicit forms, surface coverage, printing.
Gershon Elber, "Line Art Illustrations of Parametric and Implicit Forms," IEEE Transactions on Visualization and Computer Graphics, vol. 4, no. 1, pp. 71-81, Jan.-March 1998, doi:10.1109/2945.675655
Usage of this product signifies your acceptance of the Terms of Use.